Although the name might scare people away, Japanesewithanime actually has a really in-depth post that covers this topic. I'll just quote the relevant part discussing why your guess was right, but there's a ton more information, so you might want to read through it.
The na of na-adjectives is actually a copula. The prenominal copula, or attributive copula.
Basically, da だ is the copula you use in an independent clause, while na な is the copula you use in an attributive clause, also called adjectival clause. A clause that describes nouns.
But there isn't a negative form of な, so you have to go back to だ.
The negative form of na-adjectives is literally just replacing the normal copula by a negative copula such as denai でない, dewanai ではない or its contraction, janai じゃない.
He includes a link talking about the difference in usage between ではない and でない
